On the relationship between individual and group decisions

Each member of a group receives a signal about the unknown state of the world and decides on a utility-maximizing recommendation on the basis of that signal. The individuals have identical preferences. The group makes a decision that maximizes the common utility function assuming perfect pooling of the information in individual signals. An action profile is a group action and a recommendation from each individual. A collection of action profiles is rational if there exists an information structure under which all elements in the collection arise with positive probability. With no restrictions on the information structure, essentially all action profiles are rational. In fact, given any distribution over action profiles, it is possible to find an information structure that approximates the distribution. In a monotone environment in which individuals receive conditionally independent signals, essentially any single action profile is rational, although some collections of action profiles are not. © 2014 Joel Sobel

Fair social decision under uncertainty and belief disagreements

This paper aims to address two issues related to simultaneous aggregation of utilities and beliefs. The first one is related to how to integrate both inequality and uncertainty considerations into social decision making. The second one is related to how social decision should take disagreements in beliefs into account. To accomplish this, whereas individuals are assumed to abide by Savage model’s of subjective expected utility, society is assumed to prescribe, either to each individual when the ex ante individual well-being is favored or to itself when the ex post individual well-being is favored, acting in accordance with the maximin expected utility theory of Gilboa and Schmeidler (J Math Econ 18:141–153, 1989). Furthermore, it adapts an ex ante Pareto-type condition proposed by Gayer et al. (J Legal Stud 43:151–171, 2014), which says that a prospect Pareto dominates another one if the former gives a higher expected utility than the latter one, for each individual, for all individuals’ beliefs. In the context where the ex ante individual welfare is favored, our ex ante Pareto-type condition is shown to be equivalent to social utility taking the form of a MaxMinMin social welfare function, as well as to the individual set of priors being contained within the range of individual beliefs. However, when the ex post individual welfare is favored, the same Pareto-type condition is shown to be equivalent to social utility taking the form of a MaxMinMin social welfare function, as well as to the social set of priors containing only weighted averages of individual beliefs

Voting and the Cardinal Aggregation of Judgments

The paper elaborates the idea that voting is an instance of the aggregation of judgments, this being a more general concept than the aggregation of preferences. To aggregate judgments one must first measure them. I show that such aggregation has been unproblematic whenever it has been based on an independent and unrestricted scale. The scales analyzed in voting theory are either context dependent or subject to unreasonable restrictions. This is the real source of the diverse 'paradoxes of voting' that would better be termed 'voting pathologies'. The theory leads me to advocate what I term evaluative voting. It can also be called utilitarian voting as it is based on having voters express their cardinal preferences. The alternative that maximizes the sum wins. This proposal operationalizes, in an election context, the abstract cardinal theories of collective choice due to Fleming and Harsanyi. On pragmatic grounds, I argue for a three valued scale for general elections

The Case for Utilitarian Voting

Utilitarian voting (UV) is defined in this paper as any voting rule that allows the voter to rank all of the alternatives by means of the scores permitted under a given voting scale. Specific UV rules that have been proposed are approval voting, allowing the scores 0, 1; range voting, allowing all numbers in an interval as scores; evaluative voting, allowing the scores -1, 0, 1. The paper deals extensively with Arrow’s impossibility theorem that has been interpreted as precluding a satisfactory voting mechanism. I challenge the relevance of the ordinal framework in which that theorem is expressed and argue that instead utilitarian, i.e. cardinal social choice theory is relevant for voting. I show that justifications of both utilitarian social choice and of majority rule can be modified to derive UV. The most elementary derivation of UV is based on the view that no justification exists for restricting voters’ freedom to rank the alternatives on a given scale

A Voting-Based System for Ethical Decision Making

We present a general approach to automating ethical decisions, drawing on machine learning and computational social choice. In a nutshell, we propose to learn a model of societal preferences, and, when faced with a specific ethical dilemma at runtime, efficiently aggregate those preferences to identify a desirable choice. We provide a concrete algorithm that instantiates our approach; some of its crucial steps are informed by a new theory of swap-dominance efficient voting rules. Finally, we implement and evaluate a system for ethical decision making in the autonomous vehicle domain, using preference data collected from 1.3 million people through the Moral Machine website.Comment: 25 pages; paper has been reorganized, related work and discussion sections have been expande

Rational Legal Decision-Making, Value Judgment and Efficient Precaution in Tort law

By reinterpreting Savage axioms as axioms of the social rationality over resource allocations, we derive a social welfare function encompassing individual social values and a social attitude towards distributional inequality. Wealth maximization becomes the purpose of law only if individuals have equal social values and the society does not care about distributional inequality. In tort law, when the injurer is less socially valued than the victim, the society imposes a stricter due precaution level, and punitive damages will be awarded. Tort law also implicitly transfers wealth from the less socially valued party to the more socially valued party.rationality; value judgement; tort law; punitive damage

Experimental auctions, collective induction and choice shift: willingness-to-pay for rice quality in Senegal

We propose a collective induction treatment as an aggregator of information and preferences, which enables testing whether consumer preferences for food quality elicited through experimental auctions are robust to aggregation. We develop a two-stage estimation method based on social judgement scheme theory to identify the determinants of social influence in collective induction. Our method is tested in a market experiment aiming to assess consumers willingness-to-pay for rice quality in Senegal. No significant choice shift was observed after collective induction, which suggests that consumer preferences for rice quality are robust to aggregation. Almost three quarters of social influence captured by the model and the variables was explained by social status, market expertise and information

Utilitarian Collective Choice and Voting

In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow’s theorem, all voting methods must be seriously flawed. Arrow’s theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow’s result. Parallel to Arrow’s ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting. A conclusion of the paper is that the defects of conventional voting methods result not from Arrow’s theorem, but rather from restrictions imposed on voters’ expression of their preferences. The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior